The unlicensed 60 GHz band brings the promise of multi-gigabit data rates to support new applications such as high definition video over wireless links. Signal propagation in the 60 GHz band significantly differs from that in the traditionally used 2.4 and 5 GHz bands. The propagation and penetration losses in the 60 GHz band are much higher. Furthermore, the signals are often reflected in indoor settings. Previous physical layer studies show that the use of directional antennas can significantly help in coping with these effects. In this paper, we address the problem of neighbor discovery in the 60 GHz band. We account for not only discovery via direct line-of-sight paths, but also via refleected beams. To the best of our knowledge, none of the previous efforts on higher layer protocols for use with directional antennas account for reflections. We consider two approaches for neighbor discovery (a) direct discovery where each node explicitly discovers its neighbors and, (b) gossip-based discovery where nodes exchange information with regards to their already discovered neighbors. We develop analytical models to capture the performance of the two approaches and validate the models via simulations in indoor settings with obstacles that reflect the transmitted signals. As one might expect, the gossip based discovery incurs a lower neighbor-discovery latency than direct discovery. We examine the impact of system parameters such as varying beamwidth and node density. Our study provides insights on the right choice of system parameters for efficient neighbor discovery in the 60 GHz regime.